RV without a WD hitch

Possibly. From where to where? Any wind in the forecast? Any sway prevention in the F350? Year? Your profile gives NO information. Stealthy? Doesn’t matter the length of your drive. You can get blown off the highway 5 minutes from home.

New F350?

The "E4" refers to sway control device?

You do not need sway control unless you have a trailer that sways. Sway control is nice to have just in case, but
you certainly can tow any size trailer without sway control.

Make sure your ball is rated for that 11,000 lb trailer weight, some are not.

Sounds like your receiver hitch/towing set-up is ample for what you plan to tow.
The only question is will your truck self-level like many new trucks with tow packages. A 11,000 trailer will have 1,000-1.500 lbs of tongue weight so will cause the rear of truck to squat, then is when WD hitch helps, or if the truck itself can air up and level off.

It’s doable. I did it for the first season and did have sway when traveling past semis and on windy days. Nothing like I was gonna wreck or anything but it was noticeable. Now that I have one I wouldn’t go without. It makes a huge difference.

Seven hours is a long way to white-knuckle a bad setup.

Can you wait a few days to get the right equipment? There should always be time for the right gear.

I don't think a 350 SRW is gonna squat, I barely get any squat with a 3100 lb camper in the bed. You don't say what kind of trailer, a lot depends on the weight/balance when empty. Sway is caused by not enough tongue weight, 10% is the bare minimum.

For example, toy haulers have very heavy tongue weights when empty so that when you load those heavy toys behind the axles the tongue doesn't get too light. An empty toy hauler will tow great as long as your truck can handle the tongue weight.

On the other hand front kitchen models are built tongue-light so that it doesn't get too heavy on the tongue when you load in food, beer and pots/pans. Manufacturers control tongue weight using axle placement.

Chances are you'll be fine towing empty with no WD hitch on that truck. Build speed slowly and be ready with the manual switch on the trailer brakes at the first hint of sway.

Length also matters, the longer the TT the more sail area that the wind will act on, both natural gales and passing semis.

Congrats on the new TT!!

Thanks all, we are looking at the 37' rockwood/flagstaffs with the bunkhouse floor plan.

Yes the WD is weight distribution. Looking at this one https://www.amazon.com/Equal-i-zer-Progress-90-00-1000-10K-Hitch/dp/B07RZV1SJ6

We found a nice flagstaff 832bws about 6 hours away in PA (we're in CT) and we mave have a great deal to get it this weekend!

If It was me doing the towing, I think I'd be fine with it for the one trip then go the E2 route. I really can't speak for you though. An 11000 pound trailer is no light weight and I'm going to think it'll have a somewhat porky tongue weight as well. Without a WD hitch you are relying completely on the weight distribution in the coach to balance out the load. I don't think you'd have a lot issues with the tongue weight other that the occasional whoop-de-do when you come across a bridge/overpass crossing at any kind of speed on a highway...that tongue weight(w/o your E2)will push down hard on the ass-end of the pickup lightening up the front axle and steering. It's about recognizing what the hazards are due to the physics, and how you are going plan and work around them. And as the previous poster commented, make sure the ball and the ball mount are rated for this duty.

The RV transporter pulled it from Northern Indiana without WD or anti-sway, you probably can too.

What built in sway control for trailers does your new F350 have?